Does your cPanel user have the rights to create the database ? Or has the limit of number of databases been crossed ?
If you could open a support ticket with a test account we can check the issue.
http://www.softaculous.net/support

For reference, if the database name is less than 5 characters it causes the installation to fail as it cannot create a username which has a 5 character minimum.

Hi,

We have tested this on our servers and even the username with less than 5 characters are created.
Which panel are you using ?
If it is H-Sphere then you must have set some custom settings which does not allow to create username with less than 5 characters.
If you can open a support ticket with a test account details we will check the issue.